Quantum key distribution (QKD) [1]}, [2]} is by far the most practical technology in quantum information. It allows two distant parties (Alice and Bob) to establish secure keys against any eavesdropper. In recent decades, various QKD protocols have been proposed one after another [3]}. Among them, continuous-variable (CV) QKD has its own distinct advantages at a metropolitan distance [4]} due to the use of common components of coherent optical communication technology. In addition, owing to the extraordinary spectral filtering capability inherent in homodyne [5]} or heterodyne [6]} measurements, the crosstalk in wavelength division multiplexing (WDM) channels would be effectively suppressed. In this way, a single optical fiber containing multiplexing of hundreds of QKD channels and co-propagation with classical data channels will be possible, leading integration into existing communication network more efficient. In CV-QKD, discrete modulation technology has attracted much attention [7]}, [8]}, [9]}, [10]}, [11]}, [12]}, [13]}, [14]}, [15]}, [16]}, [17]}, [18]} because of its ability to reduce the requirements for modulation devices. However, due to the lack of symmetry, the corresponding security proof is more complicated. Therefore, its security proof has so far mainly relied on numerical methods [10]}, [11]}, [12]}, [14]}, [13]}, [15]}, [25]}. In fact, numerical methods are widely used to calculate the secure key rate in a large number of quantum key distribution protocols [26]}, [27]}, [28]}, [29]}, [30]}, including device-independent [31]} and measurement-device-independent [32]} protocols.
